Split singularities and the competition between crack penetration and debond at a bimaterial interface

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For a crack impinging upon a bimaterial interface at an angle, the singular stress field is a linear superposition of two modes, usually of unequal exponents, either a pair of complex conjugates, or two unequal real numbers.In the latter case, a stronger and a weaker singularity coexist (known as split singularities).We define a dimensionless parameter, called the local mode mixity, to characterize the proportion of the two modes at the length scale where the processes of fracture occur.We show that the weaker singularity can readily affect whether the crack will penetrate, or debond, the interface.